Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Given the definitions of f(x) and g(x) below, find the value of g(f(-3)). {:[f(x)=x^(2)+5x+13],[g(x)=-5x+4]:} Answer:$

Given the definitions of $f(x)$ and $g(x)$ below, find the value of $g(f(-3))$ . $\newline$ $\begin{array}{l} f(x)=x^{2}+5 x+13 \\ g(x)=-5 x+4 \end{array}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Transformations of quadratic functions

Full solution

Q. Given the definitions of

f(x)

and

g(x)

below, find the value of

g(f(-3))

.

\newline

\begin{array}{l} f(x)=x^{2}+5 x+13 \\ g(x)=-5 x+4 \end{array}

\newline

Answer:

Find $f(-3)$ : First, we need to find the value of $f(-3)$ by substituting $x$ with $-3$ in the function $f(x) = x^2 + 5x + 13$ . $\newline$ Calculation: $f(-3) = (-3)^2 + 5(-3) + 13$ $\newline$ $f(-3) = 9 - 15 + 13$ $\newline$ $f(-3) = -6 + 13$ $\newline$ $f(-3) = 7$
Calculate $g(f(-3))$ : Now that we have the value of $f(-3)$ , we can find $g(f(-3))$ by substituting the value of $f(-3)$ into the function $g(x) = -5x + 4$ .
Calculation: $g(f(-3)) = g(7) = -5(7) + 4$
$g(7) = -35 + 4$
$g(7) = -31$

More problems from Transformations of quadratic functions

Question

Solve by completing the square.

\newline

m^2 - 10m - 29 = 0

\newline

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

\newline

`m` = ____ or `m` = _____

Posted 1 month ago

Question

g(x)

g(x)

is the translation

5

f(x)=x^2

\newline

Write your answer in the form

a(x–h)^2+k

a

h

k

\newline

g(x)=

Posted 1 month ago

Question

What is the range of this quadratic function?

\newline

y = x^2 - 4x + 4

\newline

\newline

\left\{y \mid y \geq 2\right\}

\newline

\left\{y \mid y \leq 0\right\}

\newline

\left\{y \mid y \geq 0\right\}

\newline

\text{all real numbers}

Posted 1 month ago

Question

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

\newline

Posted 1 month ago

Question

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Posted 1 month ago

Question

h

\newline

h^2 + 39h = 0

\newline

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

\newline

Posted 1 month ago

Question

Write a quadratic function with zeros

-9

-7

\newline

Write your answer using the variable

x

and in standard form with a leading coefficient of

1

\newline

f(x) = \_\_\_\_\_

Posted 2 months ago

Question

Find the equation of the axis of symmetry for the parabola

y = x^2

\newline

Simplify any numbers and write them as proper fractions, improper fractions, or integers.

\newline

\underline{\hspace{3cm}}

Posted 2 months ago

Question

g(x)

g(x)

is the translation

8

f(x) = x^2

\newline

Write your answer in the form

a(x – h)^2 + k

a

h

k

\newline

g(x) =

\newline

Posted 2 months ago

Question

x

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

x =

\newline

Posted 2 months ago